Transformari liniare
Transformari liniare
Transformari liniare
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No¸tiunea de transformare liniară<br />
Transformări <strong>liniare</strong> între spa¸tii finit dimensionale<br />
Valori ¸si vectori proprii<br />
Demonstra¸tie.<br />
Au loc<br />
Deducem<br />
w = f (u) = f (<br />
=<br />
n<br />
m<br />
n<br />
xiei) =<br />
i=1<br />
xi ajifj =<br />
i=1 j=1 j=1<br />
yj =<br />
Matricea unei transformări<br />
Rela¸tia dintre rang ¸si defect<br />
Schimbarea matricei unei transformări <strong>liniare</strong><br />
n<br />
xif (ei) =<br />
i=1<br />
m n<br />
( ajixi)fj<br />
i=1<br />
n<br />
ajixi, j = 1, · · · , m (3)<br />
i=1<br />
Transformări <strong>liniare</strong>